Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation

Luo, Kai; Liu, Cheng; Tian, Qiang; Hu, Haiyan

doi:10.1007/s11071-016-2735-z

Cited by 46 publications

(22 citation statements)

References 44 publications

(102 reference statements)

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“…The geometrical relations in the shell middle surface with geometrical nonlinearity taken into account take the known form [32] 2…”

Section: Relations For Unstiffened Shellsmentioning

confidence: 99%

“…Let us consider a special case for unstiffened shallow isotropic shells of rectangular planform. In this case, the Lamé parameters will be 1, 1 AB  and the dimensionless parameters will take the following form 2 Let us note that in this variant of dimensionless parameters, in addition to setting the Lamé parameters and executing simplifications connected with the material isotropy, the expressions for the shell main curvatures [37] are chosen in a different way.…”

Section: Some Special Casesmentioning

confidence: 99%

“…Shell structures are widely used in various industries, and the study of the process of their deformation is an important task [1][2][3][4]. During operation, the shells may be subjected to various loads, and therefore it is necessary to analyze their strength, stability and non-linear vibrations.…”

Section: Introductionmentioning

confidence: 99%

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Dimensionless Models of Deformation of Stiffened Shell Structures

2018

PNRPU MB

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Original Russian Text: Karpov V.V., Semenov A.A. Dimensionless models of deformation of stiffened shell structures. PNRPU Mechanics Bulletin, 2015, no. 3, pр. 74-94. This paper suggests a variant of dimensionless parameters for a wide range of shell structures. Dimensionless parameters have been used for shallow shells of rectangular planform for a long time. There is no universal form of dimensionless relations for shells of a general type, since the Lamé parameters are different for each type of shells, as far as their values and dimensions are concerned. Therefore, the work shows the dimensionless relations for strains, stresses, forces, moments and the functional of total potential energy of deformation. These relations consider geometrical nonlinearity, transverse shears, material orthotropy, as well as the introduction of ribs according to the structural anisotropy method with their shear and torsional rigidity taken into account. The authors show a further approach to solving strength and stability problems with respect to different types of shells in dimensionless parameters. Some methods intended to solve nonlinear strength problems are not quite correct, when dimensional parameters are used (for example, the methods based on the best parameter continuation method). In dimensionless parameters, all calculation are beyond doubt, as far as their correctness is concerned. The article also provides the calculations of some shell structures in dimensionless and dimensional parameters and shows their consistency. The introduction of dimensionless parameters in the course of calculation of such structures allows to obtain more comprehensive information on the stress and strain state of shells and detect strain features for a whole range of such shells. Also, this approach is suitable for optimizing the choice of structural parameters. The authors analyze some differences in critical loads that were obtained in the dimensionless and dimensional solutions of the problem. © PNRPU

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“…The geometrical relations in the shell middle surface with geometrical nonlinearity taken into account take the known form [32] 2…”

Section: Relations For Unstiffened Shellsmentioning

confidence: 99%

Section: Some Special Casesmentioning

confidence: 99%

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Dimensionless Models of Deformation of Stiffened Shell Structures

2018

PNRPU MB

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“…Eberlein and Wriggers proposed the concepts for finite elastoplastic strains in which the multiplicative decomposition of the deformation gradient tensor to the elastic and plastic deformations is applied to express the incompressible behavior under the plastic range. Luo et al applied a two‐dimensional compressible neo‐Hookean constitutive model and a two‐dimensional incompressible Mooney‐Rivlin constitutive model to the thin shell element based on the Kirchhoff‐Love theory under the plane stress state. However, in these elements, the plane stress condition is enforced by the internal iterative algorithm at each quadrature point, and the computational cost may increase.…”

Section: Introductionmentioning

confidence: 99%

A quadrilateral shell element incorporating thickness‐stretch for nearly incompressible hyperelasticity

Yamamoto

Yamada

2019

Numerical Meth Engineering

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Summary The authors proposed a quadrilateral shell element enriched with degrees of freedom to represent thickness‐stretch. The quadrilateral shell element can be utilized to consider large deformations for nearly incompressible materials, and its performance is demonstrated in small and large deformation analyses of hyperelastic materials in this study. Formulation of the proposed shell element is based on extension of the MITC4 shell element. A displacement variation in the thickness direction is introduced to evaluate the change in thickness. In the proposed approach, the thickness direction is defined using the director vectors at each midsurface node. The thickness‐stretch is approximated by the movements of additional nodes, which are placed along the thickness direction from the bottom to the top surface. The transverse normal strain is calculated using these additional nodes without assuming the plane stress condition; hence, a three‐dimensional constitutive equation can be employed without any modification. In this work, the authors apply an assumed strain technique to the special shell element to alleviate volumetric locking for nearly incompressible materials. Several numerical examples are presented to examine the effectiveness of the proposed element.

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“…Устойчивость тороидальных оболочек при статическом нагружении рассматривается в работах [8-9, 12-17, 22, 25-29], при динамическом нагружении -в исследованиях [20][21][28][29], а в статьях [4][5][6][7][8]21] анализируются их колебания. Вопросы оптимизации то-роидальных оболочек для решения конкретных практических задач были затронуты в ра-ботах [11][12].…”

Section: Introductionunclassified

Stability of Toroidal Shell Segments at Variation of a Deflection Angle

2017

PNRPU MB

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Бакусов П.А., Семенов А.А. Устойчивость сегментов тороидальных оболочек при изменении угла отклонения от вертикальной оси // Вестник Пермского национального исследовательского политехнического университета. Механика. -2017Механика. - . -№ 3. -С. 17-36. DOI: 10.15593/perm.mech/2017 Bakusov P.A., Semenov A.A. Stability of toroidal shell segments at variation of a deflection angle. PNRPU Mechanics Bulletin, 2017, no. 3, pp. 17-36. DOI: 10.15593/perm.mech/2017 В работе исследуется устойчивость панелей стальных тороидальных тонко-стенных оболочечных конструкций с различным углом отклонения от вертикальной оси. Математическая модель (модель Тимошенко-Рейснера) является геометри-чески нелинейной и представлена в виде функционала полной потенциальной энергии деформации. Для сведения вариационной задачи к решению системы алгебраических уравнений применялся метод Ритца, для которого использовались два различных базиса: тригонометрический и полиномиальный (основан на много-членах Лежандра). Процесс формирования аппроксимирующих функций рассмот-рен подробно с учетом симметрии тороидальных панелей.Полученная в итоге система алгебраических уравнений является нелинейной и решается методом Ньютона. Алгоритм реализован в среде аналитических вы-числений Maple 2017.Проведены расчеты сегментов тороидальных оболочек при действии внешней равномерно распределенной поперечной нагрузки, и получены значения нагрузок потери устойчивости.При выборе вариантов конструкций фиксировался параметр большого радиуса для того, чтобы покрывная площадь рассматриваемого сегмента оболочки остава-лась неизменной, а малый радиус зависел от угла отклонения от вертикальной оси.В ряде случаев наблюдаются местные потери устойчивости. Проанализирова-но влияние угла отклонения от вертикальной оси на значения нагрузок потери ус-тойчивости и максимальные значения прогибов. Приводятся результаты, получен-ные для двух видов аппроксимации.Расчеты показали, что оба варианта аппроксимации дают достаточно близкие результаты при малых нагрузках, однако существенно различаются при больших.Увеличение угла отклонения приводит к уменьшению значения критической нагрузки, что может быть вызвано увеличением площади поверхности самой обо-лочки. Однако при этом уменьшается величина максимального прогиба. © ПНИПУ Ключевые слова:оболочки, устойчивость, математическая модель, тороидальные оболочки, панели, метод Ритца, многочлены Лежандра, критические нагрузки  Бакусов Павел

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Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation

Cited by 46 publications

References 44 publications

Dimensionless Models of Deformation of Stiffened Shell Structures

Dimensionless Models of Deformation of Stiffened Shell Structures

A quadrilateral shell element incorporating thickness‐stretch for nearly incompressible hyperelasticity

Stability of Toroidal Shell Segments at Variation of a Deflection Angle

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